Name: 在數學課上塗鴉。星星 (Doodling in Math Class: Stars)
Uploaded: 2021-01-14T05:16:23.000Z
Duration: 3 min 58 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

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Let's say you're me, and you're in math class,

動名詞

and you're supposed to be learning about factoring.

is a useful skill for the average person to know,

with real-world applications ranging from passing your state

exams all the way to getting a higher SAT score.

And unfortunately, does not have the time

to show you why factoring is actually interesting.

So like any reasonable person, you start doodling.

Maybe it's because your teacher's soporific voice

reminds you of a lullaby, but you're drawing stars.

It seems obvious that a five-pointed star

takes the least number of strokes to draw.

Sure, you can make a start with four points,

but that's not really a star the way you're defining stars.

because it takes two separate lines to make.

much like you can put two triangles together

to make a six-pointed star, you can put two squares together

And any even-numbered star with p points can be made out of two

that if you wanted to avoid thinking about factoring,

maybe drawing stars was not the greatest idea.

But wait, four would be an even number of points,

but that would mean you could make it out of two 2-gons.

Maybe you were taught polygons with only two sides

Sure, the four-pointed star doesn't look too star-like.

But then you realize you can make the six-pointed star out

got an asterisk, which is definitely a legitimate star.

In fact, for any star where the number of points

is divisible by 2, you can draw it asterisk style.

But that's not quite what you're looking for.

What you want is a doodle game, and here it is.

Draw p points in a circle, evenly spaced.

Starting at one point, go around the circle

and connect to the point two places over.

If you get to the starting place before you've

covered all the points, jump to a lonely point, and keep going.

And it's a successful game, in that previously you

were considering running screaming from the room.

Or the window was open, so that's an option, too.

But now, you're not only entertained but beginning

to become curious about the nature of this game.

The interesting thing is that the more points you have,

the more different ways there is to draw the star.

I happen to like seven-pointed stars because there's

two really good ways to draw them, but they're still simple.

I would like to note here that I've never actually left

Eight is interesting, too, because not only are

while another can be drawn without picking up the pencil.

And because you're me, and you're a nerd,

decide to call this kind of star a square star

Four 4-gons, two 2-gons, even the completely degenerate case

Unfortunately, five pentagons is already difficult to discern.

And beyond that, it's very hard to see and appreciate

you can make a star as a composite of smaller

stars-- that is, two boring old five-pointed stars.

Unless you count asterisk stars, in which case 8 was two

But 10 is interesting because you can make it

Then there's 11, which can't be made out of separate parts